Is there a tessellation of the plane where, given a snapshot of a region of the plane (taken at a certain resolution) it would be possible to know the coordinates of that location up to the information density of the image?
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Is there a tessellation of the plane where, given a snapshot of a region of the plane (taken at a certain resolution) it would be possible to know the coordinates of that location up to the information density of the image?
(This couldn't be infinite could it?)
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Is there a tessellation of the plane where, given a snapshot of a region of the plane (taken at a certain resolution) it would be possible to know the coordinates of that location up to the information density of the image?
(This couldn't be infinite could it?)
@futurebird To have this you would need every patch of a tiling to be unique, right? I think then if you had this you would be guaranteed to be an aperiodic tiling: since no two patches are alike, there’s no way to translate it. Conversely, my gut says that aperiodic tilings have this property at *some level*.
Also, if you allow for tesselations where each tile is unique, there’s probably something cool that could be done with fractal edges to encode position
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F myrmepropagandist shared this topic
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Is there a tessellation of the plane where, given a snapshot of a region of the plane (taken at a certain resolution) it would be possible to know the coordinates of that location up to the information density of the image?
(This couldn't be infinite could it?)
I think @ai6yr
m.ai6yr.org does this? -
Is there a tessellation of the plane where, given a snapshot of a region of the plane (taken at a certain resolution) it would be possible to know the coordinates of that location up to the information density of the image?
(This couldn't be infinite could it?)
@futurebird If the snapshot is always at the same resolution (by which I'm assuming you mean the same area), even an aperiodic tessellation will have a limited number of different configurations that can fit into the image. So the answer would be no.
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@futurebird If the snapshot is always at the same resolution (by which I'm assuming you mean the same area), even an aperiodic tessellation will have a limited number of different configurations that can fit into the image. So the answer would be no.
@futurebird Not completely sure I get what you mean when you say, up to the information density, though.
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@futurebird Not completely sure I get what you mean when you say, up to the information density, though.
The size of the snap shot in relation to the size of the map where it can give you the location?
Density is probably the wrong word. Or unhelpful.
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I think @ai6yr
m.ai6yr.org does this?@caragraph @futurebird I'm missing some context here...
But here's photos of the Earth taken from the ISS geolocated to their coordinates. You can do that with any photo from an airplane, manually.
Astronaut Photo Interactive Map
Astronaut Photo Interactive Map
(eol.jsc.nasa.gov)
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@caragraph @futurebird I'm missing some context here...
But here's photos of the Earth taken from the ISS geolocated to their coordinates. You can do that with any photo from an airplane, manually.
Astronaut Photo Interactive Map
Astronaut Photo Interactive Map
(eol.jsc.nasa.gov)
But the earth isn't a tessellated surface.
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Is there a tessellation of the plane where, given a snapshot of a region of the plane (taken at a certain resolution) it would be possible to know the coordinates of that location up to the information density of the image?
(This couldn't be infinite could it?)
@futurebird my intuition is that equilateral triangles and a pair of orthonrrmal basis vectors separated by an angle of 60 degrees for the co-ordinates are the key, since equilateral triangles can be broken down into smaller triangles, but I guess you already got that far. I don't remember enough about how to prove stuff to prove this intuition right or wrong, unfortunately.
